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Modeling the Motion of a Windmill Blade

Modeling the Motion of a Windmill Blade
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2019-03-22 02:08
FunctionTrigonometryGeometric Construction
In collections Sine and Cosine Functions
This example models the motion of a windmill blade. It involves concepts of trigonometric functions and periodic motion. Using GeoGebra commands such as If, Circle, Point, Segment, etc., a dynamic model of the windmill blade is constructed. Suitable for high school mathematics education, particularly in trigonometry and kinematics.

GeoGebra Commands & Parameters

  1. If(OffsetBlades, 240, 0) → offset
  2. Circle(A_1, radiusA) → d
  3. Point(d) → A_2
  4. If(longPost, A_1 + v + (0, 30), A_1 + v) → B_1
  5. If(¬fastSpeed, speedA, speedA + 2) → speedB
  6. If(longBlades, radiusA + 20, radiusA) → radiusB
  7. Circle(B_1, radiusB) → circle2
  8. Point(circle2) → B_2
  9. If(longPost, A_3 + v + (0, 30), A_3 + v) → B_3
  10. Segment((0, -15), (180, -15)) → mySlider
  11. Point(mySlider) → sliderPt
  12. Sequence("\hphantom{kkkkkk}", i, 1, 2) → spacers
  13. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  14. Segment((0, 0), (right, 0)) → groundLine
  15. VerticalText("\text{Height (m)}") → lblHeight
  16. Sequence(Polygon[A_1, Rotate[A_3, ((-((i * 120))))° - angleA°, A_1], Rotate[A_2, ((-((i * 120))))° - angleA°, A_1]], i, 0, 2) → blades
  17. Sequence(Polygon[B_1, Rotate[B_2, ((-((i * 120))))° - angleB°, B_1], Rotate[B_3, ((-((i * 120))))° - angleB°, B_1]], i, 0, 2) → blades2
  18. Rotate(A_2, ((-angleA))°, A_1) → RotatePointA
  19. Rotate(B_2, ((-angleB))°, B_1) → RotatePointB
  20. TableText({{"\text{Taller Tower}", "\text{Offset Blades}"}, spacers, {"\text{Longer Blades}", "\text{Faster Speed}"}}, "vl") → changeOptions